Hi, I just learn about Pythagorean identities.

As i know that cos^2θ + sin^2θ = 1

but what is the work out to get 1? and why 1?

Thanks.

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- Apr 28th 2010, 06:29 AMlex3Pythagorean identities
Hi, I just learn about Pythagorean identities.

As i know that cos^2θ + sin^2θ = 1

but what is the work out to get 1? and why 1?

Thanks. - Apr 28th 2010, 08:30 AMkompik
Consider a right triangle like here, i.e., the hypothenuse is denoted by h, opposite side is a and adjacent side is b.

Then:

sinθ=a/h

cosθ=b/h

and you know from Pythagorean theorem that $\displaystyle a^2+b^2=h^2$.

So if you calculate $\displaystyle cos^2\theta+\sin^2\theta$, you get

$\displaystyle cos^2\theta+\sin^2\theta=\frac{a^2}{h^2}+\frac{b^2 }{h^2}=\frac{a^2+b^2}{h^2}=\frac{h^2}{h^2}=1.$

You can even simplify this by rescaling the triangle so that h=1. (In case you're familiar with unit circle definitions of trigonometric functions, you should know, what I mean.)

BTW you have a whole article about this identity at wikipedia. - May 4th 2010, 03:02 AMlex3
Oh, now i understand.

Thanks mate!